This short guide explains how to install Python version 3.9.0 on a Raspberry Pi running Raspbian.

First install the dependencies needed to build

sudo apt-get update
sudo apt-get install -y build-essential tk-dev libncurses5-dev libncursesw5-dev libreadline6-dev libdb5.3-dev libgdbm-dev libsqlite3-dev libssl-dev libbz2-dev libexpat1-dev liblzma-dev zlib1g-dev libffi-dev

Compile (takes a while!)
wget https://www.python.org/ftp/python/3.9.0/Python-3.9.0.tar.xz
tar xf Python-3.9.0.tar.xz
cd Python-3.9.0
./configure --prefix=/usr/local/opt/python-3.9.0
make -j 4

Install
sudo make altinstall

And remove the files

cd ..
sudo rm -r Python-3.9.0
rm Python-3.9.0.tar.xz
. ~/.bashrc

Make Python 3.9 the default version, make aliases
sudo update-alternatives --config python

And verify:
python -V